To do probability, follow these basic steps:
- Identify the event you want to find the probability for. This could be something like rolling a "3" on a die or drawing a red card from a deck.
- Determine the total number of possible outcomes for the event. For example, a die has 6 sides, so there are 6 possible outcomes.
- Count the number of favorable outcomes - the ways the event can happen. For rolling a "3," there is only 1 favorable outcome.
- Calculate the probability using the formula:
Probability=Number of favorable outcomesTotal number of possible outcomes\text{Probability}=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}Probability=Total number of possible outcomesNumber of favorable outcomes
This will give you a value between 0 and 1, where 0 means the event cannot happen and 1 means it will definitely happen. For example, the probability of rolling a "3" on a die is 16\frac{1}{6}61
. For multiple events occurring together , such as rolling a "6" on two dice simultaneously, calculate the probability of each event separately and then multiply them:
P(A and B)=P(A)×P(B)P(A\text{ and }B)=P(A)\times P(B)P(A and B)=P(A)×P(B)
For two dice, the probability of rolling a "6" on both is 16×16=136\frac{1}{6}\times \frac{1}{6}=\frac{1}{36}61×61=361
. Additional probability rules include:
- Addition rule for "or" events:
P(A or B)=P(A)+P(B)−P(A∩B)P(A\text{ or }B)=P(A)+P(B)-P(A\cap B)P(A or B)=P(A)+P(B)−P(A∩B)
- Complement rule for "not" events:
P(not A)=1−P(A)P(\text{not }A)=1-P(A)P(not A)=1−P(A)
- Conditional probability when one event depends on another:
P(B∣A)=P(A∩B)P(A)P(B|A)=\frac{P(A\cap B)}{P(A)}P(B∣A)=P(A)P(A∩B)
These formulas help calculate probabilities in more complex situations
. In summary, probability is about measuring how likely an event is to happen by comparing favorable outcomes to total outcomes, and applying multiplication or addition rules when dealing with multiple events
